Thats only true if there is no air movement over the surface of the water or the moister content in the air is so high there is no more room for anymore water molecules.
However, consider evaporative cooling. The air moving over the surface will move the heated molecules at the water surface out of the way making room for more as they come up.(heat rises)The differential at the surface of the water now allows more room for the rapidly moving water molecules to move to. As the differential is increased at the surface(air velocity), the energy(btu) being stored in the water gradually decreases, causing a cooling(btu loss)
Think how a swamp cooler works. You can actually speed the cooling by circulating the water more, bringing the warmer water to the surface faster to increase evaporation, or increasing the velocity of the air moving over the surface. The air will "carry" the warm evaporated water molecules away, leaving behind less excited(cooler) water molecules.
Ambient heat is not the same as direct heat. Evaporative cooling isnt as effective with direct heat...so be sure to turn your heater off...obviously..
My 2¢.